# Calculus with Diffrential Equations: Pleease help?

Suppose that represents the temperature of a cup of coffee set out in a room, where T is expressed in degrees Fahrenheit and t in minutes.
A physical principle known as Newton’s Law of Cooling tells us that
dT/dt = -1/15T+5
15T + 5.
a) Supposes that T(0) = 105. What does the differential equation give us for the
value of dT
dt |T=0? Explain in a complete sentence the meaning of these two
facts.
(b) Is T increasing or decreasing at t = 0?
(c) What is the approximate temperature at t = 1?
(d) On a graph, make a plot of dT/dt as a function of T.
(e)For which values of T does T increase?
(f) What do you think is the temperature of the room? Explain your thinking.
(g) Verify that T(t) = 75 + 30e^(-t/15) is the solution to the differential equation with initial value T(0) = 105. What happens to this solution after a long time?

## Similar Questions

1. ### chem211

A chemistry professor has a cup of coffee containing 50.0mL of room temperature coffee at 25.0C. The professor also has a new pot of hot coffee at temperature of 96.0C. What volume of hot coffee will the professor need to add to
2. ### algebra

A cup of coffee is heated to 180°F and placed in a room that maintains a temperature of 65°F. The temperature of the coffee after t minutes is given by T(t) = 65 + 115e^−0.042t.(a) Find the temperature, to the nearest

Mr. Currie pours himself some coffee into a paper cup before making his way to the amusement park. The coffee temperature is 350C when the cup is placed on the kitchen counter with room temperature of 20o C. Mr. Currie was called
4. ### science -chemistry

Mr. Currie pours himself some coffee into a paper cup before making his way to the amusement park. The coffee temperature is 350C when the cup is placed on the kitchen counter with room temperature of 20o C. Mr. Currie was called
5. ### calculus

The differential equation below models the temperature of a 87°C cup of coffee in a 17°C room, where it is known that the coffee cools at a rate of 1°C per minute when its temperature is 67°C. Solve the differential equation
6. ### Calculus

Suppose that represents the temperature of a cup of coffee set out in a room, where T is expressed in degrees Fahrenheit and t in minutes. A physical principle known as Newton’s Law of Cooling tells us that dT/dt = -1/15T+5 15T
7. ### Differential equations in Calculus...plsssss help?

Suppose that represents the temperature of a cup of coffee set out in a room, where T is expressed in degrees Fahrenheit and t in minutes. A physical principle known as Newton’s Law of Cooling tells us that dT/dt = -1/15T+5 15T
8. ### statistics

Suppose the temperature of a cup of coffee is normally distributed with a mean of 142 degress F. If a cup of coffee has a z score of 1.5, which of the following is true?
9. ### math

The busy Mother pours herself a coffee into a paper cup before making her way to the amusement park. The coffee temperature is 35 C when the cup is placed on the kitchen counter. The Mother needs to tend to her son and her coffee
10. ### Chemistry

At a local convenience store, you purchase a cup of coffee, but, at 98.4oC, it is too hot to drink. You add 23.0 g of ice that is –2.2oC to 248 mL of the coffee. What is the final temperature of the coffee? (Assume the heat

More Similar Questions